I have never lost my facebook password, I do not know what could be the problem. You just put in a strong password, that's all.
Anyway, it's a good note to be aware of your account. Simple tips when logging in public places. Make sure you don't tick the box "remember password" once you enter the facebook. After you use it, logged it out right away and don't forget to delete the history *clear browser* including the tabs and recently sites you visited everything within the hour of you in using whatever that device is.